I'm trying to build a device to test a proportional valve. This valve requires a 24v input and a control signal that ranges from -10v to +10v. I've read up getting an analog voltage from a pmw signal, and read up on charge pumps to get a negative voltage. But all of this is sort theory, and I don't really understand it fully..... So what attached components would I need to do something like this? Or maybe just a research topic pointer...

Is this +/- 10V signal an input or an output. The body of the post and the title seem to contradict each other.What sort of resolution do you want?Basically you need some form of power supply, an op amp or some transistors and some filtering.

Filter PWM output to produce a smooth 0-5volt analogue signal. The centre point of your 24 volt battery configuration to be connected to arduino ground. All OpAmps to be powered by +/- 12 volts. Feed the 0-5volt analogue to a unity gain OpAmp/comparator with +2.5 volt fixed offset. This will produce -2.5 to +2.5 volt output. Now feed this to OpAmp with gain of 4 to produce the required -10 to +10 volt drive signal. Probably could be done with a single Opamp/comparator but using two makes it simpler to calibrate.

If your PWM filter reduces the 100% signal to less than 5 volts, let's say 4.5, then the 50% PWM value should be 2.25 so you need to alter the 1st stage bias voltage to +2.25 and the output will be -2.25 to +2.25. By altering the gain of the second stage to 4.44 you get back to the -10 to +10 output.

The datasheet says that the input is a differential amplifier. Therefore, one way of controlling the valve is to use two PWM pins, generate a 0 -> 10V signal from each one, and feed them to the inputs. Set one of the outputs to zero (depending on which way you want to move the valve) and the other to 0 to 10V. This requires 2 PWM pins to control the valve, but does not need a negative supply. The attached schematic is one way of generating one 0-10V signal.

Alternatively, only use a PWM pin to generate one of the inputs, and switch the other to 0V or +10V from a digital output pin.

If my german is good enough its a 0..10V control signal. But it is _differential_ so you can connect either Ue or Ud to ground and get either sense as (Ud-Ue) is the control voltage (section 3.3.1.3 of the pdf) - anyone got a better grasp of technical german??

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No but if you scroll down the data sheet the bottom half is repeated in English!

So yes it is a differential input. That means the two signals both go from 0 to 10V, it is just that when one is up and the other is down that is a 10V signal but when this is reversed it is a -10V input. But there is not a -10V with respect to ground it is just with respect to the other signal.Therefore you need two 0 to 10V analogue signals. I would put the PWM first through a transistor to get it in the 0 to 10V range, and then filter it to remove the PWM switching noise. This is simpler than smoothing it and then having to get a linear amplifier to boost it up to 10V.